Tips for Quantitative Courses

Overview

Quantitative courses pose unique design challenges, both on-campus and online. Some considerations to keep in mind as designing these courses are:

• The majority of course goals are skills-based rather than knowledge-based, so a large amount of time must be devoted to practice

• A class section may have a wide range of student backgrounds and comfort levels with quantitative skills, which can cause challenges with instructional pacing and social learning activities

• Depending on the program, students may struggle with motivation, especially if quantitative courses are rare in the curriculum (for example, the lone research statistics course in a nursing program)

• Quantitative courses are structured very differently from non-quantitative courses, so students who do not have strong quantitative backgrounds may not have developed the metacognitive strategies necessary for success

The asynchronous and synchronous online teaching model can be very effective for quantitative courses. The following guidelines will help you make design decisions that leverage the async/sync approach to best support your students.

Assessments

Use diagnostic assessments in the asynchronous material to better understand student background.

• Consider including a diagnostic assessment in the first week of your course, particularly if students may have previous exposure to topics in your course.

• Identify advanced students and students who may need extra support early, and use this information to tailor your live session plans.

Create ungraded or low-stakes assessments, like practice quizzes and problem sets, in the asynchronous materials to provide additional practice and to keep track of student progress.

• Leverage autograding when possible so that students have automatic feedback on their performance.

• When autograding is not an option, provide sample solutions, distributed either alongside the practice quiz or problem set, or provided at a designated time, such as after the live session.

Avoid having one large, high-stakes exam. Use projects, problem sets, or several lower-stakes tests instead.

• Include multiple assessments in your course, spaced so that students receive feedback before the next assessment, so that they have opportunities to learn from their mistakes.

• Consider allowing students to recoup part of their grade after a test by correcting problems and resubmitting.

If group projects are an appropriate assessment for your learning objectives, use information from diagnostic assessments to assign groups strategically.

• The approach to structuring student groups should depend on the project and on the range of ability.

• If students are able to choose their project topic, it may be beneficial to group students by ability, so that advanced students can choose a more complex project.

• If students are all working on the same project, and the gap in ability is moderate, it may be advantageous to mix the groups in ability, so that more experienced students can help less experienced students.

Slowly increase the complexity of problems given to students, but be clear about the level of difficulty students should expect on exams, graded homework, or projects.

• When students are first learning a new skill, break a problem into smaller parts, or provide easier, less complex problems.

• As students gain confidence and experience, ramp up complexity by making problems more challenging or adding additional context, such as using word problems.

• Clearly identify which problems are purely instructional and which problems are similar to what students must solve to be successful in the course.

Synchronous Instruction

Use polls at the start of class to better understand how students are doing.

• Ask students how long their homework took to complete

• Have students complete a short problem and answer via a poll

• Test student recall by asking a conceptual question in a poll

Avoid lecturing in the live session.

• Introduce topics and skills in asynchronous video and text segments that can be referenced and re-watched by students as they continue building their quantitative skills

• Reserve the synchronous session for problem solving activities so that students have the opportunity to practice and receive formative feedback

• Lecture in the synchronous session may occasionally be appropriate if you have an advanced class that would like to discuss something not covered in the asynchronous material, or if you have evidence that your students did not understand a topic covered in the asynchronous material and need additional explanation

Use student performance on diagnostic and formative assessments to customize live session activities.

• For a class with more advanced students, have more complex examples and topics ready to discuss

• If students struggle with a problem in a formative assessment, devote time to work through the problem in class

• Although you should still design generalized live session plans for quantitative courses, make them flexible so that you can always adapt to student needs.

Encourage students to ask questions in advance of the live session that can be addressed during class time.

• Using an asynchronous discussion forum to gather questions allows students to see if their peers have similar questions

• Students may also help each other and resolve questions before class

Work through problems live in front of students, so that students can see your problem-solving approach and ask questions as they come up.

• Use whiteboards and screen sharing to enable live problem-solving

• Consider asking for student volunteers to tell you what to do next in a problem, or to take over solving a sub-part of the problem

• Narrate every step as you do it, and don’t be afraid to make mistakes or admit when the problem is challenging

Use breakout groups for in-class problem solving activities.

• Split students into small groups, either randomly or according to ability

• Visit each group to provide support and to check in on progress

• Pick a group to present the solution based on your observations of progress

Asynchronous Instruction

Design with the assumption that there will be a wide range of student ability.

• Focus on the learning objectives for the course as you design the asynchronous materials, and be mindful of the overall workload, as some students may spend much more time on problem solving activities than others

• If you identify advanced topics you would like to cover if time allows, either build them in the asynchronous material and clearly mark them as optional, or plan to discuss them in live sessions if time allows

Use stories, examples, and reflective exercises to boost motivation and build confidence.

• Think about (or ask) your students why they chose to take this course or enroll in this program, and use that information to select examples and stories that are relevant to their interests and motivation

• Share stories from your own work and life that students will likely relate to, such as examples of times when you made mistakes or struggled to learn a concept that you have now mastered

• Ask students rhetorical questions in your lectures to prompt them to think about why they chose to take the course, how it relates to their life and current of future careers

• Consider using discussion forums to generate dialog among students about their interests and what they are finding challenging

Work through problems in asynchronous videos.

• Break problem-solving techniques into small, discrete steps, and narrate your thought process as you complete each step

• Be mindful that steps that may be intuitive to you but may not be apparent to students

• Ask students to follow along and solve the problems alongside you, and pause to give them time to think of their own solution or problem-solving approach before you share yours

Keep videos short, and use descriptive titles for videos that the students will likely need to reference.

• Quantitative lecture material can be dense, especially when teaching problem solving techniques

• Isolate topics and techniques that students will likely to need to reference as they complete assignments or projects, and film these in isolated, clearly titled video segments

• Consider building reference pages with formulas and theorems introduced in longer lecture videos

Include post-processing reflection activities to help students identify metacognitive strategies that support their learning.

• Each week, ask students to reflect on their learning experience and how they approached their assignments, especially how they worked through challenges

• Encourage students to try different study approaches and problem-solving strategies, and to write down what worked well and what did not

Additional Resources

2U has not endorsed these resources, and is not responsible for the content within the links. We share them in the hope that they might be useful.

• Kahn Academy, a free online resource with tutorials on specific quantitative topics. These can be useful external resources for struggling students.

• Math.Typeit.org, a free online tool that lets students easily generate scannable mathematical notation. The tool can be used to facilitate realtime collaboration in live session, as well as generating legible homework or assignments for easy digital grading.